An Interior-Point Algorithm for Linearly Constrained Optimization

We describe an algorithm for optimization of a smooth function subject to general linear constraints. An algorithm of the gradient projection class is used, with the important feature that the \projection" at each iteration is performed using a primal-dual interior point method for convex quadratic programming. Convergence properties can be maintained even if the projection is done inexactly in a well-deened way. Higher-order derivative information on the manifold deened by the apparently active constraints can be used to increase the rate of local convergence.